Definition 6.1 ([1]}) 
Let \(G\)  be a compact Lie group. Assume further that \(G\)  is connected and simply
connected. A quasi-Hamiltonian (or q-Hamiltonian) \(G\) -space is a \(G\) -manifold
\(M\)  together with an invariant 2-form \(\omega \,\in \, \Omega ^2(M)^G\)  and a \(G\) -equivariant map \(\mu \,\in \,C^\infty (M,\,G)\)  (where \(G\)  acts on itself by conjugation) such that:
